📚 Year 11 CAIE Chemistry: Formula & Theorem Quick Reference Handbook | 剑桥Year 11化学：公式定理速查手册
This handbook is your one‑stop revision tool for the essential formulas, relationships, and fundamental theorems required in the CAIE Year 11 Chemistry course (typically IGCSE or O Level). Whether you are tackling quantitative chemistry, energetics, rates, or equilibrium, having these equations at your fingertips will sharpen your problem‑solving skills and boost your exam confidence. Each entry is paired with a brief, contextual explanation so you understand not just what to plug in, but why the formula works.
本手册是你复习CAIE Year 11化学（通常对应IGCSE或O Level）核心公式、数量关系和基本原理的一站式工具。不论你面对的是量化计算、能量变化、速率还是平衡问题，随时查阅这些方程都能提升解题速度与考试信心。每一条公式都配有简洁的背景说明，帮助你不仅知道代入什么数字，更理解公式背后的化学逻辑。
1. The Mole & Molar Mass | 摩尔与摩尔质量
mole (symbol: mol) is the SI unit for amount of substance. One mole contains exactly 6.02 × 10²³ elementary entities (Avogadro constant, Nₐ). The molar mass (M) is the mass of one mole of a substance in grams per mole (g mol⁻¹), numerically equal to the relative atomic mass (Aᵣ) or relative formula mass (Mᵣ).
摩尔（符号 mol）是物质的量的SI单位。1摩尔精确包含6.02 × 10²³个基本单元（阿伏伽德罗常数 Nₐ）。摩尔质量 M 是1摩尔物质的质量，单位为g mol⁻¹，数值上等于相对原子质量Aᵣ或相对分子质量Mᵣ。
n = m / M
where n = amount (mol), m = mass (g), M = molar mass (g mol⁻¹). Rearrange freely: m = n × M or M = m / n.
其中 n = 物质的量 (mol)，m = 质量 (g)，M = 摩尔质量 (g mol⁻¹)。可任意变形：m = n × M 或 M = m / n。
2. Molar Volume of a Gas | 气体摩尔体积
At room temperature and pressure (r.t.p., defined as 20 °C and 1 atm), one mole of any gas occupies 24 dm³ (24 000 cm³). Under standard temperature and pressure (s.t.p., 0 °C, 1 atm), the molar volume is 22.4 dm³. For CAIE, 24 dm³ mol⁻¹ at r.t.p. is the default unless stated otherwise.
在常温常压下（r.t.p.，定义为20 °C，1 atm），任何气体的摩尔体积都是24 dm³（24 000 cm³）。在标准状况下（s.t.p.，0 °C，1 atm），摩尔体积为22.4 dm³。CAIE考试除非特别说明，默认使用r.t.p.下的24 dm³ mol⁻¹。
V (dm³) = n × 24 or n = V / 24
Use V in dm³. If volume is given in cm³, divide by 1000 first.
体积V使用dm³作单位。若题目给的是cm³，先除以1000换算。
3. Concentration of Solutions | 溶液浓度
Concentration expresses how much solute is dissolved in a given volume of solution. The most common units are mol dm⁻³ (molarity) and g dm⁻³.
浓度表示一定体积溶液中溶解了多少溶质，最常用的单位是mol dm⁻³（摩尔浓度）和g dm⁻³。
c = n / V or n = c × V
where c = concentration (mol dm⁻³), n = moles of solute, V me of solution (dm³). For concentration in g dm⁻³, simply divide mass (g) by volume (dm³).
其中 c = 浓度 (mol dm⁻³)，n = 溶质的物质的量，V = 溶液体积 (dm³)。若求质量浓度 (g dm⁻³)，直接用溶质质量 (g) 除以溶液体积 (dm³)。
4. Empirical & Molecular Formula | 实验式与分子式
The empirical formula gives the simplest whole‑number ratio of atoms in a compound. The molecular formula shows the actual number of atoms of each element in a molecule and is a whole‑number multiple of the empirical formula.
实验式（最简式）表示化合物中各元素原子的最简整数比。分子式表示分子中每种原子的实际数目，是实验式的整数倍。
Steps to find empirical formula:
求实验式的步骤：
- Convert mass (or percentage) of each element to moles: n = m / M.
- 将各元素的质量（或百分含量）换算成物质的量：n = m / M。
- Divide each mole value by the smallest number of moles to get the simplest ratio.
- 用最小的物质的量值去除各值，得最简整数比。
- Write the formula using the ratio as subscripts.
- 将比值作为下标写出实验式。
Molecular formula = (empirical formula) × n, where n = Mᵣ (molecular mass) / mass of empirical formula unit.
分子式 = (实验式) × n，其中 n = Mᵣ (分子质量) / 实验式单元的质量。
5. Percentage Yield & Atom Economy | 产率与原子经济性
Percentage yield measures the efficiency of a reaction by comparing the actual mass of product obtained to the theoretical maximum mass predicted from stoichiometry.
产率衡量反应的效率，通过比较实际获得的产品质量与根据化学计量关系算出的理论最大质量。
% Yield = (actual yield / theoretical yield) × 100
Atom economy considers how much of the reactants ends up in the desired product, a key principle of green chemistry.
原子经济性考量的是反应物中有多少原子最终进入了目标产物，这是绿色化学的核心原则。
% Atom Economy = (Mᵣ of desired product / sum of Mᵣ of all reactants) × 100
Higher atom economy means less waste.
原子经济性越高，意味着废料越少。
6. Thermochemistry: Enthalpy Change | 热化学：焓变
Enthalpy change (ΔH) is the heat energy transferred in a reaction at constant pressure. Exothermic reactions release heat (ΔH negative); endothermic reactions absorb heat (ΔH positive). The most practical formula for solution or combustion experiments uses q = mcΔT.
焓变（ΔH）是恒压条件下反应中转移的热量。放热反应的ΔH为负值，吸热反应的ΔH为正值。在溶液或燃烧实验中，最实用的计算公式是 q = mcΔT。
q = m c ΔT
where q = heat energy (J), m = mass of water or solution (g), c = specific heat capacity (4.2 J g⁻¹ °C⁻¹ for water), ΔT = temperature change (°C).
其中 q = 热能 (J)，m = 水或溶液的质量 (g)，c = 比热容（水为4.2 J g⁻¹ °C⁻¹），ΔT = 温度变化 (°C)。
Then ΔH = –q / n (exothermic gives negative sign if you define q as heat released by reaction). The 'n' is moles of the limiting reactant or the fuel burned. Always include a sign and units: kJ mol⁻¹.
然后按 ΔH = –q / n 计算（放热反应中如果q是反应释放的热量，需加负号）。'n' 用限制反应物或燃料燃烧的物质的量。始终写上正负号和单位 kJ mol⁻¹。
7. Bond Energy Calculations | 键能计算
Bond energy (bond enthalpy) is the energy required to break one mole of covalent bonds in gaseous molecules. For a reaction:
键能（键焓）是打断气态分子中1摩尔共价键所需的能量。对于一个反应：
ΔH ≈ Σ (bonds broken) – Σ (bonds formed)
Breaking bonds is endothermic (positive), making bonds is exothermic (negative). A positive overall ΔH indicates an endothermic reaction; a negative ΔH indicates an exothermic reaction.
断裂化学键吸热（正值），形成化学键放热（负值）。总的ΔH为正表明反应吸热；ΔH为负表明反应放热。
8. Electrolysis: Faraday's Laws | 电解：法拉第定律
Electrolysis uses direct current to drive non‑spontaneous chemical reactions. The quantity of electricity (Q) is related to current and time.
电解利用直流电驱动非自发的化学反应。电量 Q 与电流和时间有关。
Q = I × t
where Q = charge (coulombs, C), I = current (amperes, A), t = time (seconds, s).
其中 Q = 电荷量 (C)，I = 电流 (A)，t = 时间 (s)。
One mole of electrons carries 96 500 C (Faraday constant, F sited or liberated at an electrode can be found by combining Q = It and the electrode half‑equation.
1摩尔电子的电量 = 96 500 C（法拉第常数 F）。电极上析出的物质的量可由 Q = It 和电极半反应方程式结合求出。
n(e⁻) = Q / F and n(product) = n(e⁻) / z
where z the number of electrons needed to form one particle of the product (e.g. 2 for Cu²⁺ → Cu).
其中 z 是生成一个产物粒子所需的电子数（例如 Cu²⁺ → Cu 需要 z = 2）。
9. Rate of Reaction | 反应速率
The rate of a chemical reaction measures how quickly a reactant is consumed or a product is formed. It can be expressed as a change in quantity per unit time.
化学反应速率描述反应物消耗或产物生成的快慢，通常用单位时间内某物理量的变化来表示。
Average rate = Δ(quantity) / Δt
Common quantities include mass loss (for a gas escaping), volume of gas produced, colour change (measured by absorbance), or concentration change.
常用的物理量包括质量减少（气体逸出时）、生成气体的体积、颜色变化（测吸光度）或浓度变化。
Collision Theory (Theorem): rticles must collide with sufficient energy (≥ activation energy) and correct orientation.
碰撞理论（原理）： 反应发生的条件是粒子必须发生碰撞，且碰撞能量不小于活化能，并具有合适的取向。
10. Dynamic Equilibrium & Le Chatelier's Principle | 动态平衡与勒夏特列原理
A reversible reaction reaches dynamic equilibrium in a closed system when the rates of the forward and reverse reactions are equal. The concentrations of reactants and products remain constant but not necessarily equal.
可逆反应在封闭体系中达到动态平衡时，正反应与逆反应速率相等。反应物与产物的浓度不再变化，但不一定相等。
Le Chatelier's Principle: If a system at equilibrium experiences a change in concentration, pressure or temperature, the equilibrium position shifts to partially counteract the imposed change.
勒夏特列原理： 如果处于平衡状态的体系受到浓度、压强或温度的改变，平衡位置会向减弱这种改变的方向移动。
- Increase reactant concentration → equilibrium shifts to products (right).
- 增大反应物浓度 → 平衡右移。
- Increase pressure (for gases) → shifts to side with fewer gas moles.
- 增大压强（气体反应） → 平衡向气体分子数少的方向移动。
- Increase temperature → shifts in endothermic direction (ΔH positive).
- 升高温度 → 平衡向吸热方向移动（ΔH为正）。
- Catalyst: speeds up both forward and reverse reactions equally; it does not shift equilibrium position but helps the system reach equilibrium faster.
- 催化剂：同等程度加快正逆反应速率；不移动平衡位置，但能使体系更快达到平衡。
11. Acids, Bases & pH | 酸、碱与pH
pH is a logarithmic measure of hydrogen ion concentration in aqueous solution.
pH是水溶液中氢离子浓度的对数度量。
pH = –log₁₀[H⁺]
where [H⁺] is in mol dm⁻³. A low pH (0–2) indicates a strong acid; a high pH (12–14) indicates a strong base. Pure water has [H⁺] = 1.0 × 10⁻⁷ mol dm⁻³, so pH = 7.
其中[H⁺]单位为mol dm⁻³。低pH (0–2) 表示强酸；高pH (12–14) 表示强碱。纯水[H⁺] = 1.0 × 10⁻⁷ mol dm⁻³，因此pH = 7。
Neutralisation Theorem: Base → Salt + Water. In aqueous solution, the ionic equation is H⁺(aq) + OH⁻(aq) → H₂O(l).
中和反应原理： 酸 + 碱 → 盐 + 水。在水溶液中，离子方程式为 H⁺(aq) + OH⁻(aq) → H₂O(l)。
12. Periodicity & Group Trends (Key Theorems) | 周期性与主族递变规律（核心原理）
While not strictly formulas, understanding periodic trends is essential for predicting chemical behaviour.
虽然不是严格意义上的公式，但理解周期表递变规律对预测化学行为至关重要。
- Atomic radius decreases across a period (nuclear charge increases, electrons pulled closer) and increases down a group (extra electron shells).
- 原子半径在同周期中从左到右减小（核电荷增加，电子被拉得更近），在同族中从上到下增大（电子层数增加）。
- Ionisation energy generally increases across a period (harder to remove an electron) and decreases down a group (outer electron further from nucleus).
- 电离能在同周期中从左到右总体上增大（移去电子变得更难），在同族中从上到下减小（最外层电子离核更远）。
- Electronegativity increases across a period and decreases down a group, following the same rationale.
- 电负性在同周期中从左到右增大，在同族中从上到下减小，遵循相同的解释。
- Reactivity of metals increases down Group 1 (alkali metals) because the outer electron is lost more easily; reactivity of halogens decreases down Group 17 because it becomes harder to gain an electron.
- 金属活动性在IA族（碱金属）中从上到下增强，因为失电子越来越容易；卤素（VIIA族）的活动性从上到下减弱，因为得电子越来越难。
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